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arXiv · 2309.00392

A decidable expansion of $(\Gamma,+,F)$ with the independence property

Françoise Point
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Abstract

Let $(\Gamma,+,F)$ be a finitely generated $\mathbb Z[F]$-module where $F$ is an injective endomorphism of the abelian group $\Gamma$. We restrict ourselves to a finite automa presentable subclass, introduced by J. Bell and R. Moosa in "F-sets and finite automata. J. Th\'eor. Nombres Bordeaux 31 (2019), no. 1, 101-130" and define an expansion containing the $\mathcal F$-sets defined by R. Moosa and T. Scanlon in "Am. J. Math. 126 (2004), no. 3, p. 473-522", where every automatic subset is definable.

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Françoise Point. 2023-09-01. A decidable expansion of $(\Gamma,+,F)$ with the independence property. https://arxiv.org/abs/2309.00392

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